Lecture 33 of 41
Ray Tracing, Part 2 of 2:
Distributed RT & Radiosity/RT Hybrid Systems
William H. Hsu
Department of Computing and Information Sciences, KSU
KSOL course pages: http://bit.ly/hGvXlH / http://bit.ly/eVizrE
Public mirror web site: http://www.kddresearch.org/Courses/CIS636
Instructor home page: http://www.cis.ksu.edu/~bhsu
Readings:
Last class: Ray Tracing Handout
Today: Chapter 15, Eberly 2e – see http://bit.ly/ieUq45; Ray Tracing Handout
Next class: Tufte Handout 1
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Lecture Outline
 Reading for Last Class: Ray Tracing Handout
 Reading for Today: Chapter 15, Eberly 2e; Ray Tracing Handout
 Reading for Next Class: Tufte Handout 1
 Last Time: Ray Tracing Lab
 ACM SIGGRAPH demo: http://bit.ly/cIlgx2
 POV-Ray: http://www.povray.org
 Today: Ray Tracing, Part 2 of 2
 Hybrid global illumination: RT with radiosity
 Calculating specular exponents
 Pre-rendering backgrounds
 Progressive refinement
 Other optimizations
 Next Class: Visualization, Part 1 of 3 – Data
 Source: The Visual Display of Quantitative Information, 2e
 Applications: scientific visualization, information visualization
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Where We Are
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Acknowledgements:
Advanced Ray Tracing & Radiosity
David K. Buck, Aaron Collins, et al.
Developers
Persistence of Vision Raytracer (POV-Ray)
http://www.povray.org
C. Khambamettu & Mani V. Thomas
Professor, Department of Computing and
Information Sciences, University of Delaware &
Ph.D. graduate (University of Delaware) / Research
Scientist, Canfield Scientific
http://www.cis.udel.edu/~chandra/
http://vims.cis.udel.edu/~mani/
Mario Costa Sousa
Associate Professor
Department of Computer Science
University of Calgary
http://pages.cpsc.ucalgary.ca/~mario/
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Review [1]:
Recursive Ray Tracing Algorithm
 Compute 3D ray into scene for each 2D image pixel
 Compute 3D intersection point of ray with nearest
object in scene
 Test each primitive in the scene for intersection
 Find nearest intersection
 Recursively spawn rays from point of intersection
 Shadow Rays
 Reflected rays
 Transmitted rays
 Accumulate color from each spawned ray at point of
intersection
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Review [2]:
Distributed Ray Tracing
Adapted from slides © 2001 D. Shreiner & B. Grantham, SCU
COEN 290: Computer Graphics I, Winter 2001 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Review [3]:
Java-Based 2-D RT Demo, SIGGRAPH
Point
Light
Source
S/L
I
T
R
T
Screenshots from Java program © 2001 G. S. Owen & Y. Liu, GSU
ACM SIGGRAPH Ray Trace Java Demo – http://bit.ly/cIlgx2
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Review [4]:
POV-Ray
“Dissolution“ © 2005 Newt
http://bit.ly/fVqj5d
“The Wet Bird“ © 2001 Gilles Tran
http://bit.ly/gMBuGt
"Thanks for all the fish“ © 2008 Robert McGregor
http://bit.ly/fE04gm
Images © respective authors, generated using POV-Ray
© 1991 – 2011 D. K. Buck et al. – http://www.povray.org
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Formulas:
Ray-Object Intersection
 Intersection with plane
 Implicit form
F x, y, z   ax  by  cz  d  n  x  d
 Intersection
n  S  n  c t  d  0  t 
 d  n S
n c
 Intersection with sphere
 Implicit form
p  pc  r 2
2
p  x, y, z , p c  (a, b, c)
 Intersection
t  c  S  pc  
c  S  pc 2  c 2 S  pc 2  r 2 
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Formulas:
Light Vectors aka Shadow Rays
 “Shadow feelers”
 Spawn ray from P to each light source
 If there is intersection of shadow ray with any object then P is in
shadow
 Reflection
 Angle of incidence = angle of reflection

n 
  n    a  n
m
a

n
2

 n
n
n


ˆ n
ˆ
 a  n
n 1
r  e   m   a  m    m   a  2m
 a  2a  nˆ nˆ
ˆ cos180  1 n
ˆ  a  n
ˆ n
ˆ
  a n
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Formulas:
Refraction of Transmitted Ray
 Ray passing through two media
 Different refractive indices
 Ray bends towards/away from normal
 Snell’s Law
 ni and nr are refractive indices of two media
ni sin i  nr sin  r
 Transmitted ray
T


ni
n
u   cos  r  i cos i n
nr
nr


Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Speeding Up RT Using Extents/BVs [1]:
Motivation
 Ray tracing slow, performs same functions repeatedly
 Most time spent in computing intersections
 Each ray should be intersected with every object in scene
 Each ray spawns out reflected/transmitted rays which have to be
interested with objects in scene
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Speeding Up RT Using Extents/BVs [2]:
Definition & Basic Idea
 Extent (aka bounding volume) of object: shape that encloses it
 Compute complicated intersections if and only if ray hits extent
 Two shapes most commonly used as extents
 Sphere – specified by center and radius (C, r)
 Box – specified by sides aligned to coordinate axis
 Axis-aligned bounding box (AABB) – more typical for RT
 Oriented bounding box (OBB)
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Super-Sampling
 Instead of shooting one ray per pixel, shoot four rays through
corners of pixel
 Adaptive super-sampling (Whitted’s approach)
 Shoot more rays through corners with higher intensity
variation
 Compute final color as weighted average rather than regular
average
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Advanced Topics in RT:
Road Map




Monte Carlo Methods: Distributed RT
Bidirectional Ray Tracing: Caustics
POV-Ray
Hybrid Global Illumination
 RT: good for
 Specular highlights (highlights)
 Point-to-point interobject reflectance, shadows
 Radiosity: good for
 Diffuse reflectance (matte effects)
 Patch-to-patch interobject reflectance
 Best of both worlds
 RT for exponents
 Radiosity for backgrounds
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [1]:
What Is It?
 Distributed ray tracing: not RT on distributed systems!
 Ray tracing method
 based on randomly distributed oversampling
 to reduce aliasing artifacts
 in rendered images
 Reference
 Allen Martin, Worcester Polytechnic Institute (WPI)
 Examples for shadows, reflection, transparency
Regular RT
Distributed RT
Regular RT
Distributed RT
Regular RT
Distributed RT
“Distributed Ray Tracing” © 1995 A. Martin – http://bit.ly/ex5ZUm
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [2]:
From Stochastic RT to Distributed RT
Adapted from slide © 2005 D. Luebke, University of Virginia
CS 551-0003/651-0001: Advanced CG, Spring 2005 – http://bit.ly/eTWYAo
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [3]:
Stochastic Oversampling (Cook, 1984)
 Developed by Cook et al. (“Distributed Ray Tracing”,
Computer Graphics, vol. 18, no. 3, pp 137-145, 1984)
 Stochastic Oversampling: http://bit.ly/eTWYAo
Pixel for antialiasing
Light source for soft shadows
Reflection function for soft (glossy) reflections
Time for motion blur
Lens for depth of field
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [4]:
Gloss
 Partially reflecting surfaces
 Traditional ray tracing
 reflections look identical to scene they are reflecting
 reflections are always sharp
 Randomly distributing rays reflected by surface
 Send out packet of rays around reflecting direction
 Actual value of reflectance is statistical mean of the values
returned by each of these rays
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [5]:
Perturbing Specular Reflection Ray
 Distributing set of reflection rays by randomly
perturbing ideal specular reflection ray
 Spread of distribution determines glossiness
where wider distribution spread models
rougher surface
“Realistic Raytracing” © 2003 Z. Waters & E. Agu, WPI
http://bit.ly/gUNeGr
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [6]:
Multiple Reflected Rays
 First image is from traditional ray tracer
 Second one uses 16 rays in place of single reflected ray
 Third image uses 64 rays
“Monte Carlo Ray Tracing”
© 2005 D. Strock, University of Wisconsin Milwaukee
http://bit.ly/fSIYsL
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [7]:
Soft Shadows & Reflection
“Realistic Raytracing” © 2003 Z. Waters & E. Agu, WPI
http://bit.ly/gUNeGr
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [8]:
Fuzzy Translucency
 Same as glossy reflections, but jitter refracted ray
 Analytical function similar to shading
 Transmission function is used instead of reflectance function
 Light is gathered from other side of surface.
 Cast randomly distributed rays in general direction of
transmitted ray from traditional ray tracing
 Average value computed from each of these rays: true
translucent component
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [9]:
Soft Reflection & Transparency
 First image is obtained from traditional ray tracer
 Second image uses 10 rays for transmitted ray
 Third image uses 20 rays
“Distributed Ray Tracing” © 1995 A. Martin – http://bit.ly/ex5ZUm
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [10]:
Shadows, Reflection, Transparency
 First image is from traditional ray tracer
 Second one uses 16 rays in place of single reflected ray
 Third image uses 64 rays
“Monte Carlo Ray Tracing”
© 2005 D. Strock, University of Wisconsin Milwaukee
http://bit.ly/fSIYsL
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [11]:
Penumbras (Soft Shadows)
 Traditional ray tracing shadows: discrete
 Shadow feelers used to check if point is in shadow with respect to
point light source
 Incorrect for large light sources and/or light sources that are
close to object
 Transition from fully shadowed to partially shadowed is gradual
 Due to finite area of real light sources
 Also due to scattering of light of other surfaces
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [12]:
Tracing Penumbras (Soft Shadows)
 Set of rays cast about projected area of light source
 Projected area helps tackle large area light source
 Amount of light transmitted by: ratio of number of rays that hit
source to number of rays cast
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [13]:
Shadow Feelers & Penumbras
“Realistic Raytracing” © 2003 Z. Waters & E. Agu, WPI
http://bit.ly/gUNeGr
 In case of point source, occluder would create sharp shadow
boundary
 In area light source or if light source is closer to object
 Creation of penumbra region
 Sending out shadow feelers to capture penumbra region
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [14]:
Example – Transitions inside Penumbra
“Realistic Raytracing” © 2003 Z. Waters & E. Agu, WPI
http://bit.ly/gUNeGr
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [15]:
Example – Soft Shadows
Regular RT
Distributed RT
© 2000 A. G. Zaferakis, UNC Chapel Hill
COMP 238, Advanced Image Generation – http://bit.ly/fGYzgw / http://bit.ly/dNQHtH
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [16]:
Depth of Field
 Distance at which objects appear in focus
 Objects too far away or too close appear unfocused, blurry
 Pinhole camera model does not truly mimic real world
 Pinhole assumed to be infinitely small
 Changing focal length changes field of view but does not
change focus
“Realistic Raytracing” © 2003 Z. Waters & E. Agu, WPI
http://bit.ly/gUNeGr
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [17]:
Creating Depth of Field
 Distributed RT: places artificial lens in front of view plane
 Randomly distributed rays: used once again to simulate
blurring of depth of field
 First ray cast not modified by lens
 Focal point of lens is at fixed distance along this ray
 Rest of rays sent out for same pixel scattered about surface
of lens
 Points in scene close to focal point of lens: in sharp focus
 Points closer or further away: blurred
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [18]:
Example – Depth of Field
Low Focal Distance, © 2004 S. C. Mikula (http://bit.ly/fK6ckX)
High Focal Distance, © 2004 S. C. Mikula (http://bit.ly/fKA3b3)
Intermediate Focal Distance, © 2003 A. Bair (http://bit.ly/faXUFh)
© 2001-2006 respective authors, University of Illinois at Urbana-Champaign
CS 419, Advanced Computer Graphics – http://bit.ly/e0UfsN
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [19]:
Motion Blur
 Temporal sampling rather than spatial sampling
 Frame represents average of scene during time that camera
shutter is open
 Before each ray is cast, objects are translated or rotated to
their correct position for that frame
 Rays are averaged to give actual value
 Objects with most motion will have most blurring in rendered
image
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [20]:
Example – Motion Blur
© 2005 C. M. Cameron, University of Illinois at Urbana-Champaign
CS 419, Advanced Computer Graphics – http://bit.ly/hmZU3x
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Distributed Ray Tracing [21]:
Example – Soft Shadows
© 2005 M. A. Townsend, University of Illinois at Urbana-Champaign
CS 419, Advanced Computer Graphics – http://bit.ly/dL8GrH
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Bidirectional Ray Tracing [1]:
Example – Caustic
caustic
© 1996 H. W. Jensen, University of California, San Diego
http://graphics.ucsd.edu/~henrik/
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Bidirectional Ray Tracing [2]:
Example – Caustic
 Caustic – (concentrated) specular
reflection/refraction onto diffuse surface
 Standard ray tracing cannot handle caustics
caustic
© 1996 H. W. Jensen, University of California, San Diego
http://graphics.ucsd.edu/~henrik/
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Light Paths:
Abbreviated Notation
 Shown: interactions of light ray
 Can be expressed using regular expressions
 L: light source
 E: eye/camera
 D: diffuse surface
 S: specular surface
Sillion, F. X. & Puech, C. (1994). Radiosity and Global
Illumination. San Francisco, CA: Morgan-Kaufmann.
Amazon: http://amzn.to/evNBJH
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
BRDF Revisited: Diffuse Surfaces [1]
 Uncertainty in direction photon will take for diffuse surfaces
 Specular surfaces: Bidirectional Reflectance Distribution
Function (probability that incoming photon will leave in
particular direction) has thin profile
 Can predict direction of outgoing photon
 For ideal diffuse surfaces, BRDF would be spherical
 Photon can travel along any direction with equal probability
Sillion, F. X. & Puech, C. (1994). Radiosity and Global
Illumination. San Francisco, CA: Morgan-Kaufmann.
Amazon: http://amzn.to/evNBJH
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
BRDF Revisited: Diffuse Surfaces [2]
 Idea: Trace forward light rays into scene as well as backward
eye rays
 At diffuse surfaces, light rays additively “deposit” photons
in radiosity textures, or “rexes”, where they are picked up
by eye rays
 Rays of forward and backward pass "meet in middle" to
exchange information
Heckbert, P. S. (1990). “Adaptive radiosity textures for bidirectional ray tracing”, Proceedings of the
17th Annual Conference on Computer Graphics and Interactive Techniques (Scott 1990).
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity
 Handling cases such as LD*E
 “Color Bleeding”
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Software Packages
 Two excellent, full-featured rendering & modeling packages
 POV-Ray (http://www.povray.org/)
 Persistence of Vision Ray Tracer
 Free rendering tool (not modeling tool)
 Uses text-based scene description language (SDL)
 Available on Windows, Linux, Mac OS
 Blender (http://www.blender3d.org)
 Modeling, animation, rendering tool
 Especially useful in 3-D game creation
 Available for Windows, Linux, Irix, Sun Solaris, FreeBSD or
Mac OS X under GPL
Adapted from slides © 2005 M. Thomas & C. Khambamettu, U. Del.
CISC 440/640: Computer Graphics, Spring 2005 – http://bit.ly/hz1kfU
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [1]:
Basic Idea
 “Radiosity" method: basis is field of thermal heat transfer
 Heat transfer theory describes radiation as transfer of energy
from surface when that surface has been thermally excited
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [2]:
Derivation of Radiosity Equation
 Radiosity equation describes amount of energy which can be
emitted from surface, as sum of
 energy inherent in surface (e.g., light source)
 energy which strikes surface, being emitted from some
other surface
 Energy which leaves surface j and strikes another surface i is
attenuated by two factors
 “form factor” between surfaces i and j, which accounts for
physical relationship between two surfaces
 the reflectivity of surface i, which will absorb some
percentage of light energy striking surface
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [3]:
Radiosity Equation
Bi  Ei  i  B j Fij
Radiosity of surface i
Form Factor of
surface j
relative to
surface i
Radiosity of surface j
Emissivity of surface i
accounts for physical
relationship between
two surfaces
Reflectivity of surface i
Surface j
will absorb certain percentage of
light energy which strikes surface
Surface i
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [4]:
Implementation, Pros & Cons
 Classic radiosity = finite element method
 Assumptions
 Diffuse reflectance
 Usually polygonal surfaces
 Advantages
 Soft shadows and indirect lighting
 View independent solution
 Precompute for set of light sources
 Useful for walkthroughs
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [5]:
Classic Radiosity Algorithm
Mesh Surfaces into Elements
Compute Form Factors
Between Elements
Solve Linear System
for Radiosities
Reconstruct and
Display Solution
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [6]:
Form Factors Illustrated
Purely geometric relationship, independent of
viewpoint or surface attributes
Surface j
Surface i
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [7]:
Formula – Form Factor
angle between Normali and r
differential area of surface I, j
angle between Normalj and r
FdAj dA j 
cos  i cos  j
r
Surface j
2
j
i
dA j
r
dAi
vector from dAi to dAj
Surface i
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [8]:
Formula – Overall Form Factor
Overall form factor between i
and j is found by integrating
1
Fij 
Ai

cos  i cos  j
Ai A j
r
2
Surface j
dAi dA j
j
i
dA j
r
dAi
Surface i
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [9]:
Progressive Refinement
 Each element in scene maintains two energy values
 Accumulated
 Residual (“unshot”)
 Choose one element as shooter
 Test visibility of every other element from this shooter
 If visible, calculate shooter-to-receiver energy transfer
 Based on shooter’s residual, receiver’s reflectance
 Progressive refinement: reset residual, repeat with new shooter
 Terminate when shooter residuals below threshold
Adapted from GPU Gems 2, Chapter 39, “Global Illumination Using Progressive Refinement
Radiosity”, © 2005 G. Coombe & M. Harris, nVidia Corporation – http://bit.ly/hXQ8Zd
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [10]:
Example – Progressive Refinement
Myszkowski, K. (2001). Efficient and Predictive Realistic Image Synthesis.
Habilitation thesis, Warsaw University of Technology – http://bit.ly/gij9k6
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
POLITECHNIKA
WARSZAWSKA
Computing & Information Sciences
Kansas State University
Radiosity [11]:
Example – Cornell Box
 This simulation of the Cornell
box was done by Michael F.
Cohen and Donald P.
Greenberg for the 1985 paper
The Hemi-Cube, A Radiosity
Solution for Complex
Environments, Vol. 19, No. 3,
July 1985, pp. 31-40.
 The hemi-cube allowed form
factors to be calculated using
scan conversion algorithms
(which were available in
hardware), and made it possible
to calculate shadows from
occluding objects.
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [12]:
Example – Discontinuity Meshing
 Dani Lischinski, Filippo
Tampieri and Donald P.
Greenberg created this image
for the 1992 paper Discontinuity
Meshing for Accurate Radiosity.
 It depicts a scene that
represents a pathological case
for traditional radiosity images,
many small shadow casting
details.
 Notice, in particular, the
shadows cast by the windows,
and the slats in the chair.
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [13]:
Example – Focused Opera Lighting
 This scene from La Bohème
demonstrates the use of
focused lighting and angular
projection of predistorted
images for the background.
 It was rendered by Julie O'B.
Dorsey, Francois X. Sillion, and
Donald P. Greenberg for the
1991 paper Design and
Simulation of Opera Lighting
and Projection Effects.
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [14]:
Formula – Overall Form Factor
 These two images were rendered by
Michael F. Cohen, Shenchang Eric
Chen, John R. Wallace and Donald
P. Greenberg for the 1988 paper A
Progressive Refinement Approach
to Fast Radiosity Image Generation.
 The factory model contains 30,000
patches, and was the most complex
radiosity solution computed at that
time.
 The radiosity solution took
approximately 5 hours for 2,000
shots, and the image generation
required 190 hours; each on a
VAX8700.
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Radiosity [15]:
Example – Cornell Virtual Museum
 Most of the illumination that comes
into this simulated museum arrives
via the baffles on the ceiling.
 As the progressive radiosity
solution executed, users could
witness each of the baffles being
illuminated from above, and then
reflecting some of this light to the
bottom of an adjacent baffle.
 A portion of this reflected light was
eventually bounced down into the
room.
 The image appeared on the
proceedings cover of SIGGRAPH
1988.
© 1988-1989 E. Chen & M. Cohen,
Cornell University – http://bit.ly/e7Y1tj
Adapted from slides © 2001 - 2005 M. C. Sousa, University of Calgary
CPSC 591/691: Rendering, Spring 2001 through Spring 2011 – http://bit.ly/ftMP0G
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Summary
 Reading for Last Class: Ray Tracing Handout
 Reading for Today: Chapter 15, Eberly 2e; Ray Tracing Handout
 Reading for Next Class: Tufte Handout 1
 Last Time: Ray Tracing Lab
 ACM SIGGRAPH demo: http://bit.ly/cIlgx2
 2-D “screen”
 Moveable objects: transparent, opaque (both reflective)
 POV-Ray (http://www.povray.org) Example Renderings
 Next Class: Visualization Part 1 of 3
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University
Terminology
 Caustic: Envelope of Light Rays Reflected/Refracted by Curved Object
 RT Direction
 “Forward” RT: Light-to-Scene, Scene-to-Eye (Only for Caustics)
 “Backward” RT: Eye-to-Scene, Scene-to-Light (Typical Order)
 Bidirectional RT: both directions (meet in middle)
 Stochastic Jitter: Local Random Perturbations of Traced Rays
 Distributed RT: Nonlocal Randomization
 Penumbra: Region Where Only Part of Light Source Blocked
 Blurring
 Soft shadows: blurred penumbras (achieved using shadow feelers)
 Gloss: property of smooth surface material (multiple reflected rays)
 Reflections: soften (also distributed RT)
 Transparency: lensed caustic effect (also distributed RT)
 Form Factor: Fraction of Energy Leaving Surface i That Reaches j
 Radiosity: Heat Transfer-Based Global Illumination Method
CIS 536/636
Introduction to Computer Graphics
Lecture 33 of 41
Computing & Information Sciences
Kansas State University